From Trajectories to Activities: A Spatio-Temporal Join Approach*

Kexin Xie, Ke Deng, Xiaofang Zhou

School of Information Technology & Electrical EngineeringUniversity of Queensland

Brisbane, Australia｛kexin, dengke, zxf}@itee.uq.edu.au

University

Cafe

Restaurant A

Petrol Shop

Fast Food

SupermarketRestaurant B

ParkT_1 T_2

T_3

9:30 17:3018:00

18:4519:00

20:00

T_4

T_5

T_6

T_7

T_8

17:40

17:50

17:55

* This work is partially supported by Microsoft Research Asia Internet Services Theme Research Program

Activity Sequences

• What do we do each day?

• E.g.

‣ Drink after work?

‣ Drunk after semester ends?

‣ Jogging for 1 hour every Saturday?

‣ Watching movie after 4 hours of shopping?

‣ Only have one meal everyday during semester breaks?

‣ Sleep when the sun rises?

Data Mining with Activity Sequences

• Technique => Knowledge

‣ Frequent Sequential Pattern => Common Behavior (e.g. Collaborative promotions)

‣ Periodic Pattern => Periodic Behavior (e.g. POI suggestion)

‣ Outlier Detection => Odd Behavior (e.g. Criminal Investigation)

‣ Clustering => Similar Behavior (e.g. Friend suggestion)

• The Problem?

Spend $80 or more at Gardencity,

Get 20% Discount for

movie tickets

Data Mining with Activity Sequences

• Technique => Knowledge

‣ Frequent Sequential Pattern => Common Behavior (e.g. Collaborative promotions)

‣ Periodic Pattern => Periodic Behavior (e.g. POI suggestion)

‣ Outlier Detection => Odd Behavior (e.g. Criminal Investigation)

‣ Clustering => Similar Behavior (e.g. Friend suggestion)

• The Problem?

‣ Facebook vs Twitter

Spend $80 or more at Gardencity,

Get 20% Discount for

movie tickets

Data Mining with Activity Sequences

• Technique => Knowledge

‣ Frequent Sequential Pattern => Common Behavior (e.g. Collaborative promotions)

‣ Periodic Pattern => Periodic Behavior (e.g. POI suggestion)

‣ Outlier Detection => Odd Behavior (e.g. Criminal Investigation)

‣ Clustering => Similar Behavior (e.g. Friend suggestion)

• The Problem?

‣ Facebook vs Twitter

‣ How to obtain the activity sequences?

Spend $80 or more at Gardencity,

Get 20% Discount for

movie tickets

Travel Sequences

• Guess activity from travel sequences

‣ From office to a bar every workday.

‣ Stay at night club for 5 hours twice a year.

‣ Moving slightly faster than working speed in the park every Saturday.

‣ Moving slowly in shopping center for 4 hours then stays in a cinema.

• Where can we get such travel sequences?

‣ GPS-enabled mobile devices

From Trajectory to Sequence of Activities

• Problem

‣ Given a set of trajectories and a set of POIs, find the sequence of activities that might be performed during those set of trajectories

• Rationale

‣ If the user stays at a POI for long enough time, them some activity may take place.

• Question

‣ Which POIs did the user stay?

‣ What activities the user performed?

An Influence Model

• Given a set of POIs P, a segment of trajectory T is influenced by a p ∈ P if for every point pt on T, there does not exists a point p’ ∈ P, dist(pt, p’) < dist(pt, p).

• The influence duration of a POI p given a segment of trajectory T influenced by p, is the timestamp difference of T.

Influence Example

University

Cafe

Restaurant A

Petrol Shop

Fast Food

SupermarketRestaurant B

ParkT_1 T_2

T_3

9:30 17:3018:00

18:4519:00

20:00

T_4

T_5

T_6

T_7

T_8

17:40

17:50

17:55

Study@University Shopping@Supermarket Dining@Restaurant_B

Trajectories to Activities using Influence Duration• How long is long enough?

‣ Different POI have different requirement

‣ e.g. Fast food restaurant vs Luxury restaurant

• Which activity took place?

‣ Different activity requires different time length

‣ e.g. Working in restaurant vs Dining in restaurant

POI-Activity Mapping Set

A POI-Activity Mapping Set (PAMS) is a set of quadruple M = {(p, e, tmin, tmax)}, where p is some POI, e is some activity, and tmin, tmax are the minimum and maximum elapsed time for user activity e happened at p.

Assign User Activities

• Influence duration are checked agains tmin and tmax in PAMS

• Multiple activities may happen.

E.g. Given a subtrajectory Ts influenced by POI pi with influence duration 50, the PAMS is given as follow:

The possible activity are:

• a and b

• b

• c

Trajectory Semantic Join

• Input: A set of trajectories ST, A set of POIs P and a PAMS M

• Output: All subtrajectory-activity doubles (Ts, e), such that e may happen at Ts

( )

(T_1, (Studying@University ORWorking@University)), (T_2, Shopping@Supermarket), (T_3, Dining@Restaurant)

University

Cafe

Restaurant A

Petrol Shop

Fast Food

SupermarketRestaurant B

ParkT_1 T_2

T_3

9:30 17:3018:00

18:4519:00

20:00

T_4

T_5

T_6

T_7

T_8

17:40

17:50

17:55

Filter and Refine Approach

• Filter: Trajectory-POI join - find all subtrajectory-POI pairs that activities may took place

• Refine: assign possible events to these subtrajectory-POI pairs

University

Cafe

Restaurant A

Petrol Shop

Fast Food

SupermarketRestaurant B

ParkT_1 T_2

T_3

9:30 17:3018:00

18:4519:00

20:00

T_4

T_5

T_6

T_7

T_8

17:40

17:50

17:55

University

Cafe

Restaurant A

Petrol Shop

Fast Food

SupermarketRestaurant B

ParkT_1 T_2

T_3

9:30 17:3018:00

18:45

19:00

20:00

T_4

T_5

T_6

T_7

T_8

17:40

17:50

17:55

Trajectory Semantic Join using Voronoi Diagram

• Voronoi Diagram

‣ A Voronoi diagram of a set of points P is the subdivision of the plain into n cells, one of each site in P, with the property that a point q lies in the cell corresponding to a site pi if and only if dist(p, pi) < dist (q, pj) for each pj ∈ P, with j ≠ i.

• Computes Voronoi Diagram

‣ Fortune’s Algorithm to Compute Voronoi diagram in O(n log n) time.

(V0, t0)

(v1, t1)

(v2, t2)(v3, t3)

(v4, t4)

x1

x2

x3

P1

P2

P3

P4

P5

P6

P7

Trajectory Semantic Join using Voronoi Diagram

• Voronoi Diagram

‣ A Voronoi diagram of a set of points P is the subdivision of the plain into n cells, one of each site in P, with the property that a point q lies in the cell corresponding to a site pi if and only if dist(p, pi) < dist (q, pj) for each pj ∈ P, with j ≠ i.

• Computes Voronoi Diagram

‣ Fortune’s Algorithm to Compute Voronoi diagram in O(n log n) time.

Trajectory POI Join Algorithm

TP Join (Compute Line Intersections)

• Plane-sweep for Line Intersections

‣ Line segment becomes active when intersect with the sweep line

‣ Only “active” line segments can intersect with each other

‣ Perform intersection

check between “active”

line segments

TP Join - Organize and Output

• Observation: Given a trajectory intersects Voronoi edges on a sequence of points (p0, p1, ..., pn), where ∀0≤i<n timestamp(pi, T) ≤ timestamp(pi+1, T). All consecutive points pi and pi+1 (0≤i<n) have at least one common influenced POI influencing POI pc, and the subtrajectory Ti of T, defined by pi and pi+1 is influenced by pc.

(V0, t0)

(v1, t1)

(v2, t2)(v3, t3)

(v4, t4)

x1

x2

x3

P1

P2

P3

P4

P5

P6

P7

• Temporally sorted intersection points enclosed subtrajectories are fully influenced by some POI.

Partition Based Trajectory Semantic Join (PTSJ)

• Problem with TP Join

‣ Memory based techniques

‣ Need sort Voronoi edges and segment of trajectories globally

• Partition Based TSVID Join (PTSJ)

‣ A modified algorithm from PBSM (Patel SIGMOD 96)

‣ Partition the space into smaller size grids that spatial object can be fit into memory, insert the Key-Pointer-Element (KPE) of spatial objects into each partition if their MBR overlap with the partition.

‣ Estimate number of partitions:

‣ Perform in memory technique for each partition.

‣ Repartition may be needed if not enough memory.

Partition Based Trajectory Semantic Join (PTSJ)

Partition

TP Join for each Partition

Problems with PTSJ

• Trajectories and Voronoi cells may be inserted into multiple partition entries.

• Many duplicated entries

Reuse duplicated entries

• Duplication Reuse

‣ Each KPE stores the partitions the spatial object is inserted in, when retrieve the spatial objects of the next partition, the spatial objects with duplicated KPE do not need to be loaded in to memory (save I/O cost).

‣ Order of performing computations for the partitions are important.

Number of duplicated entries

• If KPEo is duplicated with partition P and one of its opposite partitions Popp, then it must have duplicated entires in one of its adjacent partitions.

• If KPEo is duplicated with partition P and one of its disjoint partitions Pdist, then it must have duplicated entires in one of its adjacent partitions.

• Hence Ndup(P, adj(P)) ≥ Ndup(P, opp(P)) ≥ Ndup(P, disj(P))

• Hillbert order always traverse adjacent partitions one after the other.

Adjacent

Adjacent

Adjacent

Adjacent

Opposite

Opposite Opposite

Opposite

DisjointDisjointDisjointDisjoint

Disjoint

Disjoint

Disjoint

0

1 2

3 4 5

67

8 9

101112

1314

15

PTSJ+ - PTSJ with duplication reuse

• Insert KPEs of each spatial object in to each partition.

• Each KPEs include the IDs of all partitions it is inserted into.

• Partitions need to be sorted in Hillbert order.

• Do TP-Join in for each partition in Hillbert order

• Keep track of shared spatial objects

• Avoid reloading already loaded spatial objects

Experiments

• Experimental Setting

‣ POI: 6487 POIs cropped from 105725 California POIs

‣ Trajectories: simulated from California road networks

‣ Time consumed by building index, retrieving spatial objects (I/O) is measured.

Experimental Result

0

20

40

60

80

100

120

0 4000 8000 12000

Ela

psed T

ime (

sec)

Number of Trajectories

PTSJPTSJ+

0

20

40

60

80

100

120

0 5 10 15

Ela

psed T

ime (

sec)

Trajectory Length (Hours)

PTSJ+PTSJ

Conclusion

• Trajectory and Semantic Issues:

‣ Preprocessing for Data Mining

‣ Understand User Behaviours

• Future works

‣ Further Optimisations

‣ Privacy Issues

Questions?